A Novel Integral Interconnection Damping Assignment Passivity-Based Control Approach for Underactuated Inverted Pendulum System

This study explores an application of robust nonlinear control to an underactuated inverted pendulum system (UIPS), a type of underactuated mechanical system, by first transforming the perturbed system into a form of a port-controlled Hamiltonian system (PCH), then utilizing the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) methodology to achieve the stabilization of an unperturbed closed-loop PCH system with an assigned energy function that qualifies as a Lyapunov candidate at the unstable equilibrium point. From there, the problem of robustification of IDA-PBC for a perturbed closed-loop PCH system with the state-dependent input matrix of the UIPS, subject to constant matched disturbances, is addressed by adding an outer-loop controller with an additional state. This results in a new system that preserves the framework of a PCH system, rejects the disturbance, and has a new energy function that again serves as a Lyapunov function at the desired equilibrium point. This proposed methodology is called integral IDA-PBC (iIDA-PBC). The effectiveness and applicability of the proposed method are thoroughly assessed through numerical simulations and experimental validation on the UIPS. The results demonstrate the method's proficiency in handling the system’s constant matched disturbances and model inaccuracies, underscoring the potential of iIDA-PBC for broader applications in systems facing similar control challenges.